A Variationally Consistent Derivation of Microcontinuum Theories

  • Johannes MeenenEmail author
  • Holm Altenbach
  • Victor Eremeyev
  • Konstantin Naumenko
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


Micromorphic and micropolar continuum theories can be derived from the classical equations of continuum mechanics by introducing a local averaging technique into a mixed variational principle. This approach delivers the geometrically nonlinear strain measures, the equilibrium equations and the constitutive relations of the microcontinuum theory in a natural, variationally consistent way. It also allows to evaluate the residuum of the locally averaged theory with respect to the underlying classical continuum mechanics, and shows that the microcontinuum can be understood as a special kind of a representative volume element.


Microcontinuum Variational principle 


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  1. 1.
    Eringen, A.C.: Microcontinuum field theories: foundations and solids. Springer Verlag, New York Berlin Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Mindlin, R.D.: Micro-Structure in Linear Elasticity. Arch. Rat. Mech. Anal. 11, 385–414 (1962)CrossRefGoogle Scholar
  3. 3.
    Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. International Journal of Solids and Structures 46, 774–787 (2009)CrossRefGoogle Scholar
  4. 4.
    Pope, S.: Turbulent Flows. Cambridge University Press, Cambridge (2000)Google Scholar
  5. 5.
    Suhubi, E.S., Eringen, A.C.: Nonlinear theory of simple micro-elastic solids – I. International Journal of Engineering Science 2, 189–203 (1964)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johannes Meenen
    • 1
    Email author
  • Holm Altenbach
    • 2
  • Victor Eremeyev
    • 2
  • Konstantin Naumenko
    • 2
  1. 1.AachenGermany
  2. 2.Martin-Luther-University Halle-WittenbergHalleGermany

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